Information on Result #1299454
Linear OA(3219, 19760, F3, 33) (dual of [19760, 19541, 34]-code), using construction X with Varšamov bound based on
- linear OA(3215, 19754, F3, 33) (dual of [19754, 19539, 34]-code), using
- construction X applied to C([0,16]) ⊂ C([0,12]) [i] based on
- linear OA(3199, 19684, F3, 33) (dual of [19684, 19485, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 318−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(3145, 19684, F3, 25) (dual of [19684, 19539, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 318−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(316, 70, F3, 7) (dual of [70, 54, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(316, 82, F3, 7) (dual of [82, 66, 8]-code), using
- construction X applied to C([0,16]) ⊂ C([0,12]) [i] based on
- linear OA(3215, 19756, F3, 30) (dual of [19756, 19541, 31]-code), using Gilbert–Varšamov bound and bm = 3215 > Vbs−1(k−1) = 2 235396 465123 473570 793360 934961 376797 310780 491977 720821 576606 569431 032035 348745 141846 499949 594210 502523 [i]
- linear OA(32, 4, F3, 2) (dual of [4, 2, 3]-code or 4-arc in PG(1,3)), using
- extended Reed–Solomon code RSe(2,3) [i]
- Hamming code H(2,3) [i]
- Simplex code S(2,3) [i]
- the Tetracode [i]
Mode: Linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(3219, 9880, F3, 2, 33) (dual of [(9880, 2), 19541, 34]-NRT-code) | [i] | OOA Folding | |